Conditional distributivity for uni-nullnorms with continuous and Archimedean underlying t-norms and t-conorms

Article type: Research Article

Authors: Wang, Gang | Qin, Feng^{; *} | Li, Wen-Huang

Affiliations: College of Mathematics and Information Science, Jiangxi Normal University, Nanchang, PR China

Correspondence: [*] Corresponding author. Feng Qin, College of Mathematics and Information Science, Jiangxi Normal University, 330022 Nanchang, PR China. E-mail: [email protected]

Abstract: The conditional distributivity, also called restricted distributivity, is crucial for many different areas such as utility theory and integral theory. This is the because it weakens distributivity on the domain. This paper is focused on and fully characterizes the conditional distributivity for a uni-nullnorm with continuous and Archimedean underlying t-norms and t-conorm over a continuous t-conorm or a uninorm from Umin ∪ Umax with continuous underlying operators.

Keywords: Fuzzy connectives, functional equations, conditional distributivity, uni-nullnorms, uninorm

DOI: 10.3233/JIFS-181702

Journal: Journal of Intelligent & Fuzzy Systems, vol. 36, no. 3, pp. 2773-2785, 2019